ROBREG: Stata module providing robust regression estimators

robreg provides a number of robust estimators for linear regression models. Among them are the high breakdown-point and high efficiency MM-estimator, the Huber and bisquare M-estimator, and the S-estimator, each supporting classic or robust standard errors. Furthermore, basic versions of the LMS/LQS (least median of squares) and LTS (least trimmed squares) estimators are provided. Note that the moremata package, also available from SSC, is required.

Nonparametric location estimators in the randomized complete block design

Several tests for the comparison of different groups in the randomized complete block design exist. However, there is a lack of robust estimators for the location difference between one group and all the others on the original scale. The relative marginal effects are commonly used in this situation, but they are more difficult to interpret and use by less experienced people because of the different scale. In this paper two nonparametric estimators for the comparison of one group against the others in the randomized complete block design will be presented. Theoretical results such as asymptotic normality, consistency, translation invariance, scale preservation, unbiasedness, and median unbiasedness are derived. The finite sample behavior of these estimators is derived by simulations of different scenarios. In addition, possible confidence intervals with these estimators are discussed and their behavior derived also by simulations.

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^

Indicators and Estimators in P-Adaptive Boundary Elements

The paper presents the possibility of implementing a p-adaptive process with the B.E.M. Although the exemples show that good results can be obtained with a limited amount of storage and with the simple ideas explained above, more research is needed in order to improve the two main problems of the method, i.e.: the criteria of where to refine and until what degree. Mathematically based reasoning is still lacking and will be useful to simplify the decission making. Nevertheless the method seems promising and, we hope, opens a path for a series of research lines of maximum interest. Although the paper has dealt only with plane potential problem the extension to plane elasticity as well as to 3-D potential problem is straight-forward.

On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion

We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion Bt of known Hurst index H, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around H ? 0.30, a value in the subdiffusive regime.

Asymptotic optimality of RESTART estimators in highly dependable systems

Abstract We consider a wide class of models that includes the highly reliable Markovian systems (HRMS) often used to represent the evolution of multi-component systems in reliability settings. Repair times and component lifetimes are random variables that follow a general distribution, and the repair service adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly-dependable systems, the RESTART method is used for the estimation of steady-state unavailability and other reliability measures. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty involved in applying this method is finding a suitable function, called the importance function, to define the regions. In this paper we introduce an importance function which, for unbalanced systems, represents a great improvement over the importance function used in previous papers. We also demonstrate the asymptotic optimality of RESTART estimators in these models. Several examples are presented to show the effectiveness of the new approach, and probabilities up to the order of 10-42 are accurately estimated with little computational effort.

When the brain changes its mind: Interocular grouping during binocular rivalry

The prevalent view of binocular rivalry holds that it is a competition between the two eyes mediated by reciprocal inhibition among monocular neurons. This view is largely due to the nature of conventional rivalry-inducing stimuli, which are pairs of dissimilar images with coherent patterns within each eye’s image. Is it the eye of origin or the coherency of patterns that determines perceptual alternations between coherent percepts in binocular rivalry? We break the coherency of conventional stimuli and replace them by complementary patchworks of intermingled rivalrous images. Can the brain unscramble the pieces of the patchwork arriving from different eyes to obtain coherent percepts? We find that pattern coherency in itself can drive perceptual alternations, and the patchworks are reassembled into coherent forms by most observers. This result is in agreement with recent neurophysiological and psychophysical evidence demonstrating that there is more to binocular rivalry than mere eye competition.

Image recognition: Visual grouping, recognition, and learning

Vision extracts useful information from images. Reconstructing the three-dimensional structure of our environment and recognizing the objects that populate it are among the most important functions of our visual system. Computer vision researchers study the computational principles of vision and aim at designing algorithms that reproduce these functions. Vision is difficult: the same scene may give rise to very different images depending on illumination and viewpoint. Typically, an astronomical number of hypotheses exist that in principle have to be analyzed to infer a correct scene description. Moreover, image information might be extracted at different levels of spatial and logical resolution dependent on the image processing task. Knowledge of the world allows the visual system to limit the amount of ambiguity and to greatly simplify visual computations. We discuss how simple properties of the world are captured by the Gestalt rules of grouping, how the visual system may learn and organize models of objects for recognition, and how one may control the complexity of the description that the visual system computes.

A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.

Bayesian models for finding and grouping junctions

In this paper, we propose two Bayesian methods for detecting and grouping junctions. Our junction detection method evolves from the Kona approach, and it is based on a competitive greedy procedure inspired in the region competition method. Then, junction grouping is accomplished by finding connecting paths between pairs of junctions. Path searching is performed by applying a Bayesian A* algorithm that has been recently proposed. Both methods are efficient and robust, and they are tested with synthetic and real images.